How can I make the texture to appear once the game is played?
Select the cube and go to material and make 2 new material.
Select the 1st material and 
Go to texture tab
Go below in the type and change --- Image or movie
and below 3 tabs -- Texture, material, both
Click on Material
In the below image select or open your image
Mapping -- coordinates -- UV
In the N panel go to Shading and change to -- GLSL
Select the cube go to edit mode and click the face u want to texture and press u and unwrap
Go to UV/Image editor and select the image
Now change the view from solid to texture.

Go to the material and select the 2nd color and change ur color.

Change Blender render to game engine